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%I #8 Jul 13 2015 21:06:13
%S 16,24,28,42,56,70
%N Records in 5-almost prime gaps ordered by merit.
%C Next term, if it exists, is associated with indices above 100000 in A114405 and A014614. - _R. J. Mathar_, May 10 2007
%F a(n) = records in A114405/log(A014614)) = records in (A014614(n+1) - A014614(n))/log(A014614)).
%e Records defined in terms of A114405 and A014614
%e n A114405(n) A114405(n)/log(A014614(n)).
%e 1 16 16/log 32 = 10.6301699
%e 2 24 24/log 48 = 14.2751673
%e 3 8 8/log 72 = 4.30725248
%e 4 28 28/log 80 = 14.7129144
%e 5 4 4/log 108 = 1.96712564
%e 6 8 8/log 112 = 3.90392819
%e 7 42 42/log 120 = 20.2002592
%e 8 6 6/log 168 = 2.69625443
%e ...
%e 22 56 56/log 312 = 22.4524976
%p A014614 := proc(nmax) local a,i; a := [] ; i := 1 ; while nops(a) < nmax do if numtheory[bigomega](i) = 5 then a := [op(a),i] ; fi ; i := i+1 ; end: a ; end: A114405 := proc(a014614) local a,i; a := [] ; for i from 2 to nops(a014614) do a := [op(a), op(i,a014614)-op(i-1,a014614)] ; od ; a ; end: a014614 := A014614(100000) : a114405 := A114405(a014614) : Digits := 30 : rec := -1 : for i from 1 to nops(a114405) do if evalf(a114405[i]/log(a014614[i])) > rec then printf("%d, ",a114405[i]) ; rec := evalf(a114405[i]/log(a014614[i])) ; fi ; od ; # _R. J. Mathar_, May 10 2007
%Y Cf. A014614, A065516, A111870, A111871, A114403-A114411, A114412-A114422.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Nov 25 2005
%E a(6) from _R. J. Mathar_, May 10 2007
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